Optimum shapes for lightweighted mirrors

Two types of monolithic lightweight mirrors with arched backs, the center-supported single arch and the ring-supported double arch, are discussed. It is shown that, assuming a maximum permissible rms tolerance of 6 x 10 to the -6th in, the single arch mirror weighs about 50 percent of an equivalent solid mirror up to a diameter of 24 in. The single arch is relatively simple to construct and uses a simple center support. Where a better figure is required, or for larger sizes, the double arch is superior in performance to the single arch. The weight of the double arch will vary from about 50 to under 40 percent of an equivalent conventional mirror as the diameter is increased from 20 to 144 in. Further weight reduction for the double arch is possible through the reduction of the size of the support.